0115. How can we predict that 7 will be 111₂, 64 will be 1000000₂ and 1023 will be 1111111111₂?

q We know that given 3-bits we can represent 8 items (2³ = 8) or the numbers from 0 – 7, so the number 7 must be 111₂

q We know that given 6-bits we can represent 64 items (2⁶ = 64) or the numbers from 0 – 63, so the number 63 must be 111111₂ and since 64 is 1 number greater, it must be 1000000₂

q We know that given 10-bits we can represent 1024 items (2¹⁰ = 1024) or the numbers from 0 – 1023, so the number 1023 must be 1111111111₂